Topology in Fuzzy Class Theory: Basic Notions

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fuzzy Class Theory and give some links to the traditional notions of fuzzy topology.

• Type: Conference
• Year: 2007
• Where: IFSA
• Authors: Libor Behounek, Tomás Kroupa
• Keywords: Artificial Intelligence, Closed Fuzzy Sets, Fuzzy Class Theory, Fuzzy Topology, IFSA 2007